content: /* ===========================================================
   * JFreeChart : a free chart library for the Java(tm) platform
   * ===========================================================
   *
   * (C) Copyright 2000-2012, by Object Refinery Limited and Contributors.
   *
   * Project Info:  http://www.jfree.org/jfreechart/index.html
   *
   * This library is free software; you can redistribute it and/or modify it
   * under the terms of the GNU Lesser General Public License as published by
   * the Free Software Foundation; either version 2.1 of the License, or
   * (at your option) any later version.
   *
   * This library is distributed in the hope that it will be useful, but
   * WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
   * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
   * License for more details.
   *
   * You should have received a copy of the GNU Lesser General Public
   * License along with this library; if not, write to the Free Software
   * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301,
   * USA.
   *
   * [Oracle and Java are registered trademarks of Oracle and/or its affiliates.
   * Other names may be trademarks of their respective owners.]
   *
   * -------------------------
   * XYDifferenceRenderer.java
   * -------------------------
   * (C) Copyright 2003-2012, by Object Refinery Limited and Contributors.
   *
   * Original Author:  David Gilbert (for Object Refinery Limited);
   * Contributor(s):   Richard West, Advanced Micro Devices, Inc. (major rewrite
   *                   of difference drawing algorithm);
   *                   Patrick Schlott
   *                   Christoph Schroeder
   *                   Martin Hoeller
   *
   * Changes:
   * --------
   * 30-Apr-2003 : Version 1 (DG);
   * 30-Jul-2003 : Modified entity constructor (CZ);
   * 20-Aug-2003 : Implemented Cloneable and PublicCloneable (DG);
   * 16-Sep-2003 : Changed ChartRenderingInfo --> PlotRenderingInfo (DG);
   * 09-Feb-2004 : Updated to support horizontal plot orientation (DG);
   * 10-Feb-2004 : Added default constructor, setter methods and updated
   *               Javadocs (DG);
   * 25-Feb-2004 : Replaced CrosshairInfo with CrosshairState (DG);
   * 30-Mar-2004 : Fixed bug in getNegativePaint() method (DG);
   * 15-Jul-2004 : Switched getX() with getXValue() and getY() with
   *               getYValue() (DG);
   * 25-Aug-2004 : Fixed a bug preventing the use of crosshairs (DG);
   * 11-Nov-2004 : Now uses ShapeUtilities to translate shapes (DG);
   * 19-Jan-2005 : Now accesses only primitive values from dataset (DG);
   * 22-Feb-2005 : Override getLegendItem(int, int) to return "line" items (DG);
   * 13-Apr-2005 : Fixed shape positioning bug (id = 1182062) (DG);
   * 20-Apr-2005 : Use generators for legend tooltips and URLs (DG);
   * 04-May-2005 : Override equals() method, renamed get/setPlotShapes() -->
   *               get/setShapesVisible (DG);
   * 09-Jun-2005 : Updated equals() to handle GradientPaint (DG);
   * 16-Jun-2005 : Fix bug (1221021) affecting stroke used for each series (DG);
   * ------------- JFREECHART 1.0.x ---------------------------------------------
   * 24-Jan-2007 : Added flag to allow rounding of x-coordinates, and fixed
   *               bug in clone() (DG);
   * 05-Feb-2007 : Added an extra call to updateCrosshairValues() in
   *               drawItemPass1(), to fix bug 1564967 (DG);
   * 06-Feb-2007 : Fixed bug 1086307, crosshairs with multiple axes (DG);
   * 08-Mar-2007 : Fixed entity generation (DG);
   * 20-Apr-2007 : Updated getLegendItem() for renderer change (DG);
   * 23-Apr-2007 : Rewrite of difference drawing algorithm to allow use of
   *               series with disjoint x-values (RW);
   * 04-May-2007 : Set processVisibleItemsOnly flag to false (DG);
   * 17-May-2007 : Set datasetIndex and seriesIndex in getLegendItem() (DG);
   * 18-May-2007 : Set dataset and seriesKey for LegendItem (DG);
   * 05-Nov-2007 : Draw item labels if visible (RW);
   * 17-Jun-2008 : Apply legend shape, font and paint attributes (DG);
   * 13-Feb-2012 : Applied patch 3450234 for bug 3425881 by Patrick Schlott and
   *               Christoph Schroeder (MH);
   * 16-Jun-2012 : Removed JCommon dependencies (DG);
   *
   */
  
  package org.jfree.chart.renderer.xy;
  
  import java.awt.Color;
  import java.awt.Graphics2D;
  import java.awt.Paint;
  import java.awt.Shape;
  import java.awt.Stroke;
  import java.awt.geom.GeneralPath;
  import java.awt.geom.Line2D;
  import java.awt.geom.Rectangle2D;
  import java.io.IOException;
  import java.io.ObjectInputStream;
  import java.io.ObjectOutputStream;
  import java.util.Collections;
  import java.util.LinkedList;
  
  import org.jfree.chart.LegendItem;
  import org.jfree.chart.axis.ValueAxis;
  import org.jfree.chart.ui.RectangleEdge;
  import org.jfree.chart.util.PaintUtilities;
  import org.jfree.chart.util.PublicCloneable;
  import org.jfree.chart.util.ShapeUtilities;
  import org.jfree.chart.entity.EntityCollection;
  import org.jfree.chart.entity.XYItemEntity;
  import org.jfree.chart.event.RendererChangeEvent;
  import org.jfree.chart.labels.XYToolTipGenerator;
  import org.jfree.chart.plot.CrosshairState;
  import org.jfree.chart.plot.PlotOrientation;
  import org.jfree.chart.plot.PlotRenderingInfo;
  import org.jfree.chart.plot.XYPlot;
  import org.jfree.chart.urls.XYURLGenerator;
  import org.jfree.chart.util.SerialUtilities;
  import org.jfree.data.xy.XYDataset;
  
  /**
   * A renderer for an {@link XYPlot} that highlights the differences between two
   * series.  The example shown here is generated by the
   * <code>DifferenceChartDemo1.java</code> program included in the JFreeChart
   * demo collection:
   * <br><br>
   * <img src="../../../../../images/XYDifferenceRendererSample.png"
   * alt="XYDifferenceRendererSample.png" />
   */
  public class XYDifferenceRenderer extends AbstractXYItemRenderer
          implements XYItemRenderer, PublicCloneable {
  
      /** For serialization. */
      private static final long serialVersionUID = -8447915602375584857L;
  
      /** The paint used to highlight positive differences (y(0) > y(1)). */
      private transient Paint positivePaint;
  
      /** The paint used to highlight negative differences (y(0) < y(1)). */
      private transient Paint negativePaint;
  
      /** Display shapes at each point? */
      private boolean shapesVisible;
  
      /** The shape to display in the legend item. */
      private transient Shape legendLine;
  
      /**
       * This flag controls whether or not the x-coordinates (in Java2D space)
       * are rounded to integers.  When set to true, this can avoid the vertical
       * striping that anti-aliasing can generate.  However, the rounding may not
       * be appropriate for output in high resolution formats (for example,
       * vector graphics formats such as SVG and PDF).
       *
       * @since 1.0.4
       */
      private boolean roundXCoordinates;
  
      /**
       * Creates a new renderer with default attributes.
       */
      public XYDifferenceRenderer() {
          this(Color.GREEN, Color.RED, false);
      }
  
      /**
       * Creates a new renderer.
       *
       * @param positivePaint  the highlight color for positive differences
       *                       (<code>null</code> not permitted).
       * @param negativePaint  the highlight color for negative differences
       *                       (<code>null</code> not permitted).
       * @param shapes  draw shapes?
       */
      public XYDifferenceRenderer(Paint positivePaint, Paint negativePaint,
                                  boolean shapes) {
          if (positivePaint == null) {
              throw new IllegalArgumentException(
                      "Null 'positivePaint' argument.");
          }
          if (negativePaint == null) {
              throw new IllegalArgumentException(
                      "Null 'negativePaint' argument.");
          }
          this.positivePaint = positivePaint;
          this.negativePaint = negativePaint;
          this.shapesVisible = shapes;
          this.legendLine = new Line2D.Double(-7.0, 0.0, 7.0, 0.0);
          this.roundXCoordinates = false;
      }
  
      /**
       * Returns the paint used to highlight positive differences.
       *
       * @return The paint (never <code>null</code>).
       *
       * @see #setPositivePaint(Paint)
       */
      public Paint getPositivePaint() {
          return this.positivePaint;
      }
  
      /**
       * Sets the paint used to highlight positive differences and sends a
       * {@link RendererChangeEvent} to all registered listeners.
       *
       * @param paint  the paint (<code>null</code> not permitted).
       *
       * @see #getPositivePaint()
       */
      public void setPositivePaint(Paint paint) {
          if (paint == null) {
              throw new IllegalArgumentException("Null 'paint' argument.");
          }
          this.positivePaint = paint;
          fireChangeEvent();
      }
  
      /**
       * Returns the paint used to highlight negative differences.
       *
       * @return The paint (never <code>null</code>).
       *
       * @see #setNegativePaint(Paint)
       */
      public Paint getNegativePaint() {
          return this.negativePaint;
      }
  
      /**
       * Sets the paint used to highlight negative differences.
       *
       * @param paint  the paint (<code>null</code> not permitted).
       *
       * @see #getNegativePaint()
       */
      public void setNegativePaint(Paint paint) {
          if (paint == null) {
              throw new IllegalArgumentException("Null 'paint' argument.");
          }
          this.negativePaint = paint;
          notifyListeners(new RendererChangeEvent(this));
      }
  
      /**
       * Returns a flag that controls whether or not shapes are drawn for each
       * data value.
       *
       * @return A boolean.
       *
       * @see #setShapesVisible(boolean)
       */
      public boolean getShapesVisible() {
          return this.shapesVisible;
      }
  
      /**
       * Sets a flag that controls whether or not shapes are drawn for each
       * data value, and sends a {@link RendererChangeEvent} to all registered
       * listeners.
       *
       * @param flag  the flag.
       *
       * @see #getShapesVisible()
       */
      public void setShapesVisible(boolean flag) {
          this.shapesVisible = flag;
          fireChangeEvent();
      }
  
      /**
       * Returns the shape used to represent a line in the legend.
       *
       * @return The legend line (never <code>null</code>).
       *
       * @see #setLegendLine(Shape)
       */
      public Shape getLegendLine() {
          return this.legendLine;
      }
  
      /**
       * Sets the shape used as a line in each legend item and sends a
       * {@link RendererChangeEvent} to all registered listeners.
       *
       * @param line  the line (<code>null</code> not permitted).
       *
       * @see #getLegendLine()
       */
      public void setLegendLine(Shape line) {
          if (line == null) {
              throw new IllegalArgumentException("Null 'line' argument.");
          }
          this.legendLine = line;
          fireChangeEvent();
      }
  
      /**
       * Returns the flag that controls whether or not the x-coordinates (in
       * Java2D space) are rounded to integer values.
       *
       * @return The flag.
       *
       * @since 1.0.4
       *
       * @see #setRoundXCoordinates(boolean)
       */
      public boolean getRoundXCoordinates() {
          return this.roundXCoordinates;
      }
  
      /**
       * Sets the flag that controls whether or not the x-coordinates (in
       * Java2D space) are rounded to integer values, and sends a
       * {@link RendererChangeEvent} to all registered listeners.
       *
       * @param round  the new flag value.
       *
       * @since 1.0.4
       *
       * @see #getRoundXCoordinates()
       */
      public void setRoundXCoordinates(boolean round) {
          this.roundXCoordinates = round;
          fireChangeEvent();
      }
  
      /**
       * Initialises the renderer and returns a state object that should be
       * passed to subsequent calls to the drawItem() method.  This method will
       * be called before the first item is rendered, giving the renderer an
       * opportunity to initialise any state information it wants to maintain.
       * The renderer can do nothing if it chooses.
       *
       * @param g2  the graphics device.
       * @param dataArea  the area inside the axes.
       * @param plot  the plot.
       * @param data  the data.
       * @param info  an optional info collection object to return data back to
       *              the caller.
       *
       * @return A state object.
       */
      @Override
      public XYItemRendererState initialise(Graphics2D g2,
                                            Rectangle2D dataArea,
                                            XYPlot plot,
                                            XYDataset data,
                                            PlotRenderingInfo info) {
  
          XYItemRendererState state = super.initialise(g2, dataArea, plot, data,
                  info);
          state.setProcessVisibleItemsOnly(false);
          return state;
  
      }
  
      /**
       * Returns <code>2</code>, the number of passes required by the renderer.
       * The {@link XYPlot} will run through the dataset this number of times.
       *
       * @return The number of passes required by the renderer.
       */
      @Override
      public int getPassCount() {
          return 2;
      }
  
      /**
       * Draws the visual representation of a single data item.
       *
       * @param g2  the graphics device.
       * @param state  the renderer state.
       * @param dataArea  the area within which the data is being drawn.
       * @param info  collects information about the drawing.
       * @param plot  the plot (can be used to obtain standard color
       *              information etc).
       * @param domainAxis  the domain (horizontal) axis.
       * @param rangeAxis  the range (vertical) axis.
       * @param dataset  the dataset.
       * @param series  the series index (zero-based).
       * @param item  the item index (zero-based).
       * @param crosshairState  crosshair information for the plot
       *                        (<code>null</code> permitted).
       * @param pass  the pass index.
       */
      @Override
      public void drawItem(Graphics2D g2,
                           XYItemRendererState state,
                           Rectangle2D dataArea,
                           PlotRenderingInfo info,
                           XYPlot plot,
                           ValueAxis domainAxis,
                           ValueAxis rangeAxis,
                           XYDataset dataset,
                           int series,
                           int item,
                           CrosshairState crosshairState,
                           int pass) {
  
          if (pass == 0) {
              drawItemPass0(g2, dataArea, info, plot, domainAxis, rangeAxis,
                      dataset, series, item, crosshairState);
          }
          else if (pass == 1) {
              drawItemPass1(g2, dataArea, info, plot, domainAxis, rangeAxis,
                      dataset, series, item, crosshairState);
          }
  
      }
  
      /**
       * Draws the visual representation of a single data item, first pass.
       *
       * @param x_graphics  the graphics device.
       * @param x_dataArea  the area within which the data is being drawn.
       * @param x_info  collects information about the drawing.
       * @param x_plot  the plot (can be used to obtain standard color
       *                information etc).
       * @param x_domainAxis  the domain (horizontal) axis.
       * @param x_rangeAxis  the range (vertical) axis.
       * @param x_dataset  the dataset.
       * @param x_series  the series index (zero-based).
       * @param x_item  the item index (zero-based).
       * @param x_crosshairState  crosshair information for the plot
       *                          (<code>null</code> permitted).
       */
      protected void drawItemPass0(Graphics2D x_graphics,
                                   Rectangle2D x_dataArea,
                                   PlotRenderingInfo x_info,
                                   XYPlot x_plot,
                                   ValueAxis x_domainAxis,
                                   ValueAxis x_rangeAxis,
                                   XYDataset x_dataset,
                                   int x_series,
                                   int x_item,
                                   CrosshairState x_crosshairState) {
  
          if (!((0 == x_series) && (0 == x_item))) {
              return;
          }
  
          boolean b_impliedZeroSubtrahend = (1 == x_dataset.getSeriesCount());
  
          // check if either series is a degenerate case (i.e. less than 2 points)
          if (isEitherSeriesDegenerate(x_dataset, b_impliedZeroSubtrahend)) {
              return;
          }
  
          // check if series are disjoint (i.e. domain-spans do not overlap)
          if (!b_impliedZeroSubtrahend && areSeriesDisjoint(x_dataset)) {
              return;
          }
  
          // polygon definitions
          LinkedList<Double> l_minuendXs    = new LinkedList<Double>();
          LinkedList<Double> l_minuendYs    = new LinkedList<Double>();
          LinkedList<Double> l_subtrahendXs = new LinkedList<Double>();
          LinkedList<Double> l_subtrahendYs = new LinkedList<Double>();
          LinkedList<Double> l_polygonXs    = new LinkedList<Double>();
          LinkedList<Double> l_polygonYs    = new LinkedList<Double>();
  
          // state
          int l_minuendItem      = 0;
          int l_minuendItemCount = x_dataset.getItemCount(0);
          Double l_minuendCurX   = null;
          Double l_minuendNextX  = null;
          Double l_minuendCurY   = null;
          Double l_minuendNextY  = null;
          double l_minuendMaxY   = Double.NEGATIVE_INFINITY;
          double l_minuendMinY   = Double.POSITIVE_INFINITY;
  
          int l_subtrahendItem      = 0;
          int l_subtrahendItemCount; // actual value set below
          Double l_subtrahendCurX   = null;
          Double l_subtrahendNextX  = null;
          Double l_subtrahendCurY   = null;
          Double l_subtrahendNextY  = null;
          double l_subtrahendMaxY   = Double.NEGATIVE_INFINITY;
          double l_subtrahendMinY   = Double.POSITIVE_INFINITY;
  
          // if a subtrahend is not specified, assume it is zero
          if (b_impliedZeroSubtrahend) {
              l_subtrahendItem      = 0;
              l_subtrahendItemCount = 2;
              l_subtrahendCurX      = x_dataset.getXValue(0, 0);
              l_subtrahendNextX     = x_dataset.getXValue(0,
                      (l_minuendItemCount - 1));
              l_subtrahendCurY      = 0.0;
              l_subtrahendNextY     = 0.0;
              l_subtrahendMaxY      = 0.0;
              l_subtrahendMinY      = 0.0;
  
              l_subtrahendXs.add(l_subtrahendCurX);
              l_subtrahendYs.add(l_subtrahendCurY);
          }
          else {
              l_subtrahendItemCount = x_dataset.getItemCount(1);
          }
  
          boolean b_minuendDone           = false;
          boolean b_minuendAdvanced       = true;
          boolean b_minuendAtIntersect    = false;
          boolean b_minuendFastForward    = false;
          boolean b_subtrahendDone        = false;
          boolean b_subtrahendAdvanced    = true;
          boolean b_subtrahendAtIntersect = false;
          boolean b_subtrahendFastForward = false;
          boolean b_colinear              = false;
  
          boolean b_positive;
  
          // coordinate pairs
          double l_x1 = 0.0, l_y1 = 0.0; // current minuend point
          double l_x2 = 0.0, l_y2 = 0.0; // next minuend point
          double l_x3 = 0.0, l_y3 = 0.0; // current subtrahend point
          double l_x4 = 0.0, l_y4 = 0.0; // next subtrahend point
  
          // fast-forward through leading tails
          boolean b_fastForwardDone = false;
          while (!b_fastForwardDone) {
              // get the x and y coordinates
              l_x1 = x_dataset.getXValue(0, l_minuendItem);
              l_y1 = x_dataset.getYValue(0, l_minuendItem);
              l_x2 = x_dataset.getXValue(0, l_minuendItem + 1);
              l_y2 = x_dataset.getYValue(0, l_minuendItem + 1);
  
              l_minuendCurX  = l_x1;
              l_minuendCurY  = l_y1;
              l_minuendNextX = l_x2;
              l_minuendNextY = l_y2;
  
              if (b_impliedZeroSubtrahend) {
                  l_x3 = l_subtrahendCurX;
                  l_y3 = l_subtrahendCurY;
                  l_x4 = l_subtrahendNextX;
                  l_y4 = l_subtrahendNextY;
              }
              else {
                  l_x3 = x_dataset.getXValue(1, l_subtrahendItem);
                  l_y3 = x_dataset.getYValue(1, l_subtrahendItem);
                  l_x4 = x_dataset.getXValue(1, l_subtrahendItem + 1);
                  l_y4 = x_dataset.getYValue(1, l_subtrahendItem + 1);
  
                  l_subtrahendCurX  = l_x3;
                  l_subtrahendCurY  = l_y3;
                  l_subtrahendNextX = l_x4;
                  l_subtrahendNextY = l_y4;
              }
  
              if (l_x2 <= l_x3) {
                  // minuend needs to be fast forwarded
                  l_minuendItem++;
                  b_minuendFastForward = true;
                  continue;
              }
  
              if (l_x4 <= l_x1) {
                  // subtrahend needs to be fast forwarded
                  l_subtrahendItem++;
                  b_subtrahendFastForward = true;
                  continue;
              }
  
              // check if initial polygon needs to be clipped
              if ((l_x3 < l_x1) && (l_x1 < l_x4)) {
                  // project onto subtrahend
                  double l_slope   = (l_y4 - l_y3) / (l_x4 - l_x3);
                  l_subtrahendCurX = l_minuendCurX;
                  l_subtrahendCurY = (l_slope * l_x1)
                          + (l_y3 - (l_slope * l_x3));
  
                  l_subtrahendXs.add(l_subtrahendCurX);
                  l_subtrahendYs.add(l_subtrahendCurY);
              }
  
              if ((l_x1 < l_x3) && (l_x3 < l_x2)) {
                  // project onto minuend
                  double l_slope = (l_y2 - l_y1) / (l_x2 - l_x1);
                  l_minuendCurX  = l_subtrahendCurX;
                  l_minuendCurY  = (l_slope * l_x3)
                          + (l_y1 - (l_slope * l_x1));
  
                  l_minuendXs.add(l_minuendCurX);
                  l_minuendYs.add(l_minuendCurY);
              }
  
              l_minuendMaxY    = l_minuendCurY;
              l_minuendMinY    = l_minuendCurY;
              l_subtrahendMaxY = l_subtrahendCurY;
              l_subtrahendMinY = l_subtrahendCurY;
  
              b_fastForwardDone = true;
          }
  
          // start of algorithm
          while (!b_minuendDone && !b_subtrahendDone) {
              if (!b_minuendDone && !b_minuendFastForward && b_minuendAdvanced) {
                  l_x1 = x_dataset.getXValue(0, l_minuendItem);
                  l_y1 = x_dataset.getYValue(0, l_minuendItem);
                  l_minuendCurX = l_x1;
                  l_minuendCurY = l_y1;
  
                  if (!b_minuendAtIntersect) {
                      l_minuendXs.add(l_minuendCurX);
                      l_minuendYs.add(l_minuendCurY);
                  }
  
                  l_minuendMaxY = Math.max(l_minuendMaxY, l_y1);
                  l_minuendMinY = Math.min(l_minuendMinY, l_y1);
  
                  l_x2 = x_dataset.getXValue(0, l_minuendItem + 1);
                  l_y2 = x_dataset.getYValue(0, l_minuendItem + 1);
                  l_minuendNextX = l_x2;
                  l_minuendNextY = l_y2;
              }
  
              // never updated the subtrahend if it is implied to be zero
              if (!b_impliedZeroSubtrahend && !b_subtrahendDone
                      && !b_subtrahendFastForward && b_subtrahendAdvanced) {
                  l_x3 = x_dataset.getXValue(1, l_subtrahendItem);
                  l_y3 = x_dataset.getYValue(1, l_subtrahendItem);
                  l_subtrahendCurX = l_x3;
                  l_subtrahendCurY = l_y3;
  
                  if (!b_subtrahendAtIntersect) {
                      l_subtrahendXs.add(l_subtrahendCurX);
                      l_subtrahendYs.add(l_subtrahendCurY);
                  }
  
                  l_subtrahendMaxY = Math.max(l_subtrahendMaxY, l_y3);
                  l_subtrahendMinY = Math.min(l_subtrahendMinY, l_y3);
  
                  l_x4 = x_dataset.getXValue(1, l_subtrahendItem + 1);
                  l_y4 = x_dataset.getYValue(1, l_subtrahendItem + 1);
                  l_subtrahendNextX = l_x4;
                  l_subtrahendNextY = l_y4;
              }
  
              // deassert b_*FastForward (only matters for 1st time through loop)
              b_minuendFastForward    = false;
              b_subtrahendFastForward = false;
  
              Double l_intersectX = null;
              Double l_intersectY = null;
              boolean b_intersect = false;
  
              b_minuendAtIntersect    = false;
              b_subtrahendAtIntersect = false;
  
              // check for intersect
              if ((l_x2 == l_x4) && (l_y2 == l_y4)) {
                  // check if line segments are colinear
                  if ((l_x1 == l_x3) && (l_y1 == l_y3)) {
                      b_colinear = true;
                  }
                  else {
                      // the intersect is at the next point for both the minuend
                      // and subtrahend
                      l_intersectX = l_x2;
                      l_intersectY = l_y2;
  
                      b_intersect             = true;
                      b_minuendAtIntersect    = true;
                      b_subtrahendAtIntersect = true;
                   }
              }
              else {
                  // compute common denominator
                  double l_denominator = ((l_y4 - l_y3) * (l_x2 - l_x1))
                          - ((l_x4 - l_x3) * (l_y2 - l_y1));
  
                  // compute common deltas
                  double l_deltaY = l_y1 - l_y3;
                  double l_deltaX = l_x1 - l_x3;
  
                  // compute numerators
                  double l_numeratorA = ((l_x4 - l_x3) * l_deltaY)
                          - ((l_y4 - l_y3) * l_deltaX);
                  double l_numeratorB = ((l_x2 - l_x1) * l_deltaY)
                          - ((l_y2 - l_y1) * l_deltaX);
  
                  // check if line segments are colinear
                  if ((0 == l_numeratorA) && (0 == l_numeratorB)
                          && (0 == l_denominator)) {
                      b_colinear = true;
                  }
                  else {
                      // check if previously colinear
                      if (b_colinear) {
                          // clear colinear points and flag
                          l_minuendXs.clear();
                          l_minuendYs.clear();
                          l_subtrahendXs.clear();
                          l_subtrahendYs.clear();
                          l_polygonXs.clear();
                          l_polygonYs.clear();
  
                          b_colinear = false;
  
                          // set new starting point for the polygon
                          boolean b_useMinuend = ((l_x3 <= l_x1)
                                  && (l_x1 <= l_x4));
                          l_polygonXs.add(b_useMinuend ? l_minuendCurX
                                  : l_subtrahendCurX);
                          l_polygonYs.add(b_useMinuend ? l_minuendCurY
                                  : l_subtrahendCurY);
                      }
                  }
  
                  // compute slope components
                  double l_slopeA = l_numeratorA / l_denominator;
                  double l_slopeB = l_numeratorB / l_denominator;
  
                  // test if both grahphs have a vertical rise at the same x-value
                  boolean b_vertical = (l_x1 == l_x2) && (l_x3 == l_x4) && (l_x2 == l_x4);
  
                  // check if the line segments intersect
                  if (((0 < l_slopeA) && (l_slopeA <= 1) && (0 < l_slopeB)
                          && (l_slopeB <= 1))|| b_vertical) {
  
                      // compute the point of intersection
                      double l_xi;
                      double l_yi;
                      if(b_vertical){
                          b_colinear = false;
                          l_xi = l_x2;
                          l_yi = l_x4;
                      }
                      else{
                          l_xi = l_x1 + (l_slopeA * (l_x2 - l_x1));
                          l_yi = l_y1 + (l_slopeA * (l_y2 - l_y1));
                      }
  
                      l_intersectX            = l_xi;
                      l_intersectY            = l_yi;
                      b_intersect             = true;
                      b_minuendAtIntersect    = ((l_xi == l_x2)
                              && (l_yi == l_y2));
                      b_subtrahendAtIntersect = ((l_xi == l_x4)
                              && (l_yi == l_y4));
  
                      // advance minuend and subtrahend to intesect
                      l_minuendCurX    = l_intersectX;
                      l_minuendCurY    = l_intersectY;
                      l_subtrahendCurX = l_intersectX;
                      l_subtrahendCurY = l_intersectY;
                  }
              }
  
              if (b_intersect) {
                  // create the polygon
                  // add the minuend's points to polygon
                  l_polygonXs.addAll(l_minuendXs);
                  l_polygonYs.addAll(l_minuendYs);
  
                  // add intersection point to the polygon
                  l_polygonXs.add(l_intersectX);
                  l_polygonYs.add(l_intersectY);
  
                  // add the subtrahend's points to the polygon in reverse
                  Collections.reverse(l_subtrahendXs);
                  Collections.reverse(l_subtrahendYs);
                  l_polygonXs.addAll(l_subtrahendXs);
                  l_polygonYs.addAll(l_subtrahendYs);
  
                  // create an actual polygon
                  b_positive = (l_subtrahendMaxY <= l_minuendMaxY)
                          && (l_subtrahendMinY <= l_minuendMinY);
                  createPolygon(x_graphics, x_dataArea, x_plot, x_domainAxis,
                          x_rangeAxis, b_positive, l_polygonXs, l_polygonYs);
  
                  // clear the point vectors
                  l_minuendXs.clear();
                  l_minuendYs.clear();
                  l_subtrahendXs.clear();
                  l_subtrahendYs.clear();
                  l_polygonXs.clear();
                  l_polygonYs.clear();
  
                  // set the maxY and minY values to intersect y-value
                  double l_y       = l_intersectY;
                  l_minuendMaxY    = l_y;
                  l_subtrahendMaxY = l_y;
                  l_minuendMinY    = l_y;
                  l_subtrahendMinY = l_y;
  
                  // add interection point to new polygon
                  l_polygonXs.add(l_intersectX);
                  l_polygonYs.add(l_intersectY);
              }
  
              // advance the minuend if needed
              if (l_x2 <= l_x4) {
                  l_minuendItem++;
                  b_minuendAdvanced = true;
              }
              else {
                  b_minuendAdvanced = false;
              }
  
              // advance the subtrahend if needed
              if (l_x4 <= l_x2) {
                  l_subtrahendItem++;
                  b_subtrahendAdvanced = true;
              }
              else {
                  b_subtrahendAdvanced = false;
              }
  
              b_minuendDone    = (l_minuendItem == (l_minuendItemCount - 1));
              b_subtrahendDone = (l_subtrahendItem == (l_subtrahendItemCount
                      - 1));
          }
  
          // check if the final polygon needs to be clipped
          if (b_minuendDone && (l_x3 < l_x2) && (l_x2 < l_x4)) {
              // project onto subtrahend
              double l_slope    = (l_y4 - l_y3) / (l_x4 - l_x3);
              l_subtrahendNextX = l_minuendNextX;
              l_subtrahendNextY = (l_slope * l_x2)
                      + (l_y3 - (l_slope * l_x3));
          }
  
          if (b_subtrahendDone && (l_x1 < l_x4) && (l_x4 < l_x2)) {
              // project onto minuend
              double l_slope = (l_y2 - l_y1) / (l_x2 - l_x1);
              l_minuendNextX = l_subtrahendNextX;
              l_minuendNextY = (l_slope * l_x4)
                      + (l_y1 - (l_slope * l_x1));
          }
  
          // consider last point of minuend and subtrahend for determining
          // positivity
          l_minuendMaxY    = Math.max(l_minuendMaxY,
                  l_minuendNextY);
          l_subtrahendMaxY = Math.max(l_subtrahendMaxY,
                  l_subtrahendNextY);
          l_minuendMinY    = Math.min(l_minuendMinY,
                  l_minuendNextY);
          l_subtrahendMinY = Math.min(l_subtrahendMinY,
                  l_subtrahendNextY);
  
          // add the last point of the minuned and subtrahend
          l_minuendXs.add(l_minuendNextX);
          l_minuendYs.add(l_minuendNextY);
          l_subtrahendXs.add(l_subtrahendNextX);
          l_subtrahendYs.add(l_subtrahendNextY);
  
          // create the polygon
          // add the minuend's points to polygon
          l_polygonXs.addAll(l_minuendXs);
          l_polygonYs.addAll(l_minuendYs);
  
          // add the subtrahend's points to the polygon in reverse
          Collections.reverse(l_subtrahendXs);
          Collections.reverse(l_subtrahendYs);
          l_polygonXs.addAll(l_subtrahendXs);
          l_polygonYs.addAll(l_subtrahendYs);
  
          // create an actual polygon
          b_positive = (l_subtrahendMaxY <= l_minuendMaxY)
                  && (l_subtrahendMinY <= l_minuendMinY);
          createPolygon(x_graphics, x_dataArea, x_plot, x_domainAxis,
                  x_rangeAxis, b_positive, l_polygonXs, l_polygonYs);
      }
  
      /**
       * Draws the visual representation of a single data item, second pass.  In
       * the second pass, the renderer draws the lines and shapes for the
       * individual points in the two series.
       *
       * @param x_graphics  the graphics device.
       * @param x_dataArea  the area within which the data is being drawn.
       * @param x_info  collects information about the drawing.
       * @param x_plot  the plot (can be used to obtain standard color
       *         information etc).
       * @param x_domainAxis  the domain (horizontal) axis.
       * @param x_rangeAxis  the range (vertical) axis.
       * @param x_dataset  the dataset.
       * @param x_series  the series index (zero-based).
       * @param x_item  the item index (zero-based).
       * @param x_crosshairState  crosshair information for the plot
       *                          (<code>null</code> permitted).
       */
      protected void drawItemPass1(Graphics2D x_graphics,
                                   Rectangle2D x_dataArea,
                                   PlotRenderingInfo x_info,
                                   XYPlot x_plot,
                                   ValueAxis x_domainAxis,
                                   ValueAxis x_rangeAxis,
                                   XYDataset x_dataset,
                                   int x_series,
                                   int x_item,
                                   CrosshairState x_crosshairState) {
  
          Shape l_entityArea = null;
          EntityCollection l_entities = null;
          if (null != x_info) {
              l_entities = x_info.getOwner().getEntityCollection();
          }
  
          Paint l_seriesPaint   = getItemPaint(x_series, x_item);
          Stroke l_seriesStroke = getItemStroke(x_series, x_item);
          x_graphics.setPaint(l_seriesPaint);
          x_graphics.setStroke(l_seriesStroke);
  
          PlotOrientation l_orientation      = x_plot.getOrientation();
          RectangleEdge l_domainAxisLocation = x_plot.getDomainAxisEdge();
          RectangleEdge l_rangeAxisLocation  = x_plot.getRangeAxisEdge();
  
          double l_x0 = x_dataset.getXValue(x_series, x_item);
          double l_y0 = x_dataset.getYValue(x_series, x_item);
          double l_x1 = x_domainAxis.valueToJava2D(l_x0, x_dataArea,
                  l_domainAxisLocation);
          double l_y1 = x_rangeAxis.valueToJava2D(l_y0, x_dataArea,
                  l_rangeAxisLocation);
  
          if (getShapesVisible()) {
              Shape l_shape = getItemShape(x_series, x_item);
              if (l_orientation == PlotOrientation.HORIZONTAL) {
                  l_shape = ShapeUtilities.createTranslatedShape(l_shape,
                          l_y1, l_x1);
              }
              else {
                  l_shape = ShapeUtilities.createTranslatedShape(l_shape,
                          l_x1, l_y1);
              }
              if (l_shape.intersects(x_dataArea)) {
                  x_graphics.setPaint(getItemPaint(x_series, x_item));
                  x_graphics.fill(l_shape);
              }
              l_entityArea = l_shape;
          }
  
          // add an entity for the item...
          if (null != l_entities) {
              if (null == l_entityArea) {
                  l_entityArea = new Rectangle2D.Double((l_x1 - 2), (l_y1 - 2),
                          4, 4);
              }
              String l_tip = null;
              XYToolTipGenerator l_tipGenerator = getToolTipGenerator(x_series,
                      x_item);
              if (null != l_tipGenerator) {
                  l_tip = l_tipGenerator.generateToolTip(x_dataset, x_series,
                          x_item);
              }
              String l_url = null;
              XYURLGenerator l_urlGenerator = getURLGenerator();
              if (null != l_urlGenerator) {
                  l_url = l_urlGenerator.generateURL(x_dataset, x_series,
                          x_item);
              }
              XYItemEntity l_entity = new XYItemEntity(l_entityArea, x_dataset,
                      x_series, x_item, l_tip, l_url);
              l_entities.add(l_entity);
          }
  
          // draw the item label if there is one...
          if (isItemLabelVisible(x_series, x_item)) {
              drawItemLabel(x_graphics, l_orientation, x_dataset, x_series,
                            x_item, l_x1, l_y1, (l_y1 < 0.0));
          }
  
          int l_domainAxisIndex = x_plot.getDomainAxisIndex(x_domainAxis);
          int l_rangeAxisIndex  = x_plot.getRangeAxisIndex(x_rangeAxis);
          updateCrosshairValues(x_crosshairState, l_x0, l_y0, l_domainAxisIndex,
                                l_rangeAxisIndex, l_x1, l_y1, l_orientation);
  
          if (0 == x_item) {
              return;
          }
  
          double l_x2 = x_domainAxis.valueToJava2D(x_dataset.getXValue(x_series,
                  (x_item - 1)), x_dataArea, l_domainAxisLocation);
          double l_y2 = x_rangeAxis.valueToJava2D(x_dataset.getYValue(x_series,
                  (x_item - 1)), x_dataArea, l_rangeAxisLocation);
  
          Line2D l_line = null;
          if (PlotOrientation.HORIZONTAL == l_orientation) {
              l_line = new Line2D.Double(l_y1, l_x1, l_y2, l_x2);
          }
          else if (PlotOrientation.VERTICAL == l_orientation) {
              l_line = new Line2D.Double(l_x1, l_y1, l_x2, l_y2);
          }
  
          if ((null != l_line) && l_line.intersects(x_dataArea)) {
              x_graphics.setPaint(getItemPaint(x_series, x_item));
              x_graphics.setStroke(getItemStroke(x_series, x_item));
              x_graphics.draw(l_line);
          }
      }
  
      /**
       * Determines if a dataset is degenerate.  A degenerate dataset is a
       * dataset where either series has less than two (2) points.
       *
       * @param x_dataset  the dataset.
       * @param x_impliedZeroSubtrahend  if false, do not check the subtrahend
       *
       * @return true if the dataset is degenerate.
       */
      private boolean isEitherSeriesDegenerate(XYDataset x_dataset,
              boolean x_impliedZeroSubtrahend) {
  
          if (x_impliedZeroSubtrahend) {
              return (x_dataset.getItemCount(0) < 2);
          }
  
          return ((x_dataset.getItemCount(0) < 2)
                  || (x_dataset.getItemCount(1) < 2));
      }
  
      /**
       * Determines if the two (2) series are disjoint.
       * Disjoint series do not overlap in the domain space.
       *
       * @param x_dataset  the dataset.
       *
       * @return true if the dataset is degenerate.
       */
      private boolean areSeriesDisjoint(XYDataset x_dataset) {
  
          int l_minuendItemCount = x_dataset.getItemCount(0);
          double l_minuendFirst  = x_dataset.getXValue(0, 0);
          double l_minuendLast   = x_dataset.getXValue(0, l_minuendItemCount - 1);
  
          int l_subtrahendItemCount = x_dataset.getItemCount(1);
          double l_subtrahendFirst  = x_dataset.getXValue(1, 0);
          double l_subtrahendLast   = x_dataset.getXValue(1,
                  l_subtrahendItemCount - 1);
  
          return ((l_minuendLast < l_subtrahendFirst)
                  || (l_subtrahendLast < l_minuendFirst));
      }
  
      /**
       * Draws the visual representation of a polygon
       *
       * @param x_graphics  the graphics device.
       * @param x_dataArea  the area within which the data is being drawn.
       * @param x_plot  the plot (can be used to obtain standard color
       *                information etc).
       * @param x_domainAxis  the domain (horizontal) axis.
       * @param x_rangeAxis  the range (vertical) axis.
       * @param x_positive  indicates if the polygon is positive (true) or
       *                    negative (false).
       * @param x_xValues  a linked list of the x values (expects values to be
       *                   of type Double).
       * @param x_yValues  a linked list of the y values (expects values to be
       *                   of type Double).
       */
      private void createPolygon (Graphics2D x_graphics,
                                  Rectangle2D x_dataArea,
                                  XYPlot x_plot,
                                  ValueAxis x_domainAxis,
                                  ValueAxis x_rangeAxis,
                                  boolean x_positive,
                                  LinkedList x_xValues,
                                  LinkedList x_yValues) {
  
          PlotOrientation l_orientation      = x_plot.getOrientation();
          RectangleEdge l_domainAxisLocation = x_plot.getDomainAxisEdge();
          RectangleEdge l_rangeAxisLocation  = x_plot.getRangeAxisEdge();
  
          Object[] l_xValues = x_xValues.toArray();
          Object[] l_yValues = x_yValues.toArray();
  
          GeneralPath l_path = new GeneralPath();
  
          if (PlotOrientation.VERTICAL == l_orientation) {
              double l_x = x_domainAxis.valueToJava2D((Double) l_xValues[0], x_dataArea,
                      l_domainAxisLocation);
              if (this.roundXCoordinates) {
                  l_x = Math.rint(l_x);
              }
  
              double l_y = x_rangeAxis.valueToJava2D((Double) l_yValues[0], x_dataArea,
                      l_rangeAxisLocation);
  
              l_path.moveTo((float) l_x, (float) l_y);
              for (int i = 1; i < l_xValues.length; i++) {
                  l_x = x_domainAxis.valueToJava2D((Double) l_xValues[i], x_dataArea,
                          l_domainAxisLocation);
                  if (this.roundXCoordinates) {
                      l_x = Math.rint(l_x);
                  }
  
                  l_y = x_rangeAxis.valueToJava2D((Double) l_yValues[i], x_dataArea,
                          l_rangeAxisLocation);
                  l_path.lineTo((float) l_x, (float) l_y);
              }
              l_path.closePath();
          }
          else {
              double l_x = x_domainAxis.valueToJava2D((Double) l_xValues[0], x_dataArea,
                      l_domainAxisLocation);
              if (this.roundXCoordinates) {
                  l_x = Math.rint(l_x);
              }
  
              double l_y = x_rangeAxis.valueToJava2D((Double) l_yValues[0], x_dataArea,
                      l_rangeAxisLocation);
  
              l_path.moveTo((float) l_y, (float) l_x);
              for (int i = 1; i < l_xValues.length; i++) {
                  l_x = x_domainAxis.valueToJava2D((Double) l_xValues[i], x_dataArea,
                          l_domainAxisLocation);
                  if (this.roundXCoordinates) {
                      l_x = Math.rint(l_x);
                  }
  
                  l_y = x_rangeAxis.valueToJava2D((Double) l_yValues[i], x_dataArea,
                          l_rangeAxisLocation);
                  l_path.lineTo((float) l_y, (float) l_x);
              }
              l_path.closePath();
          }
  
          if (l_path.intersects(x_dataArea)) {
              x_graphics.setPaint(x_positive ? getPositivePaint()
                      : getNegativePaint());
              x_graphics.fill(l_path);
          }
      }
  
      /**
       * Returns a default legend item for the specified series.  Subclasses
       * should override this method to generate customised items.
       *
       * @param datasetIndex  the dataset index (zero-based).
       * @param series  the series index (zero-based).
       *
       * @return A legend item for the series.
       */
      @Override
      public LegendItem getLegendItem(int datasetIndex, int series) {
          LegendItem result = null;
          XYPlot p = getPlot();
          if (p != null) {
              XYDataset dataset = p.getDataset(datasetIndex);
              if (dataset != null) {
                  if (getItemVisible(series, 0)) {
                      String label = getLegendItemLabelGenerator().generateLabel(
                              dataset, series);
                      String description = label;
                      String toolTipText = null;
                      if (getLegendItemToolTipGenerator() != null) {
                          toolTipText
                              = getLegendItemToolTipGenerator().generateLabel(
                                      dataset, series);
                      }
                      String urlText = null;
                      if (getLegendItemURLGenerator() != null) {
                          urlText = getLegendItemURLGenerator().generateLabel(
                                  dataset, series);
                      }
                      Paint paint = lookupSeriesPaint(series);
                      Stroke stroke = lookupSeriesStroke(series);
                      Shape line = getLegendLine();
                      result = new LegendItem(label, description,
                              toolTipText, urlText, line, stroke, paint);
                      result.setLabelFont(lookupLegendTextFont(series));
                      Paint labelPaint = lookupLegendTextPaint(series);
                      if (labelPaint != null) {
                          result.setLabelPaint(labelPaint);
                      }
                      result.setDataset(dataset);
                      result.setDatasetIndex(datasetIndex);
                      result.setSeriesKey(dataset.getSeriesKey(series));
                      result.setSeriesIndex(series);
                  }
              }
  
          }
  
          return result;
  
      }
  
      /**
       * Tests this renderer for equality with an arbitrary object.
       *
       * @param obj  the object (<code>null</code> permitted).
       *
       * @return A boolean.
       */
      @Override
      public boolean equals(Object obj) {
          if (obj == this) {
              return true;
          }
          if (!(obj instanceof XYDifferenceRenderer)) {
              return false;
          }
          if (!super.equals(obj)) {
              return false;
          }
          XYDifferenceRenderer that = (XYDifferenceRenderer) obj;
          if (!PaintUtilities.equal(this.positivePaint, that.positivePaint)) {
              return false;
          }
          if (!PaintUtilities.equal(this.negativePaint, that.negativePaint)) {
              return false;
          }
          if (this.shapesVisible != that.shapesVisible) {
              return false;
          }
          if (!ShapeUtilities.equal(this.legendLine, that.legendLine)) {
              return false;
          }
          if (this.roundXCoordinates != that.roundXCoordinates) {
              return false;
          }
          return true;
      }
  
      /**
       * Returns a clone of the renderer.
       *
       * @return A clone.
       *
       * @throws CloneNotSupportedException  if the renderer cannot be cloned.
       */
      @Override
      public Object clone() throws CloneNotSupportedException {
          XYDifferenceRenderer clone = (XYDifferenceRenderer) super.clone();
          clone.legendLine = ShapeUtilities.clone(this.legendLine);
          return clone;
      }
  
      /**
       * Provides serialization support.
       *
       * @param stream  the output stream.
       *
       * @throws IOException  if there is an I/O error.
       */
      private void writeObject(ObjectOutputStream stream) throws IOException {
          stream.defaultWriteObject();
          SerialUtilities.writePaint(this.positivePaint, stream);
          SerialUtilities.writePaint(this.negativePaint, stream);
          SerialUtilities.writeShape(this.legendLine, stream);
      }
  
      /**
       * Provides serialization support.
       *
       * @param stream  the input stream.
       *
       * @throws IOException  if there is an I/O error.
       * @throws ClassNotFoundException  if there is a classpath problem.
       */
      private void readObject(ObjectInputStream stream)
          throws IOException, ClassNotFoundException {
          stream.defaultReadObject();
          this.positivePaint = SerialUtilities.readPaint(stream);
          this.negativePaint = SerialUtilities.readPaint(stream);
          this.legendLine = SerialUtilities.readShape(stream);
      }
  
  }
  